In seismic exploration, energy that bounces back into the subsurface from interfaces such air/water (in the marine environment) or air/land (in land seismic) generate seismic arrivals called free-surface multiples. These arrivals are in general undesirable seismic events because they can mislead the interpretation of the data to properly locate subsurface geological structures with potential hydrocarbon accumulation. Removal of free-surface multiples from seismic reflection data is an important and challenging problem in seismic data processing. General methods of dealing with the mitigation of surface-related multiples include methods based on the feedback model known as surface-related multiple elimination (SRME) (Verschuur et al., 1992) and the inverse-scattering series approach (Weglein et al., 2003). In principle, these physics-based methods are capable of predicting and eliminating free-surface multiples without any prior knowledge about the subsurface velocity model. However, rigorous application of these methods requires that data are available at all offsets (distance between source and receiver) and well sampled in space and time.
In general it is very difficult to meet the data requirement for a rigorous application of the free-surface multiple elimination methods mentioned above. This is especially the case in marine seismic acquisition where near-offset gap (distance between source and the first receiver on the streamer cable) and crossline receiver spacing can be very large in comparison to the receiver spacing in the inline direction. In some situations, such as deep marine environment, near-offset missing traces can be extrapolated fairly well using kinematics-based methods (such as Radon extrapolation after application of normal moveout correction). When such near-offset extrapolation is successful, it is possible to apply SRME and obtain a good estimate of the free-surface multiple contributions to the data. Subsequently, adequate optimization approaches can be used to effectively subtract the free-surface multiples from the dataset. However in an environment where the depth from the free-surface to the first strong reflector is small, such as in a shallow marine environment where the water bottom depth is less than 100 m, extrapolation to the near offsets by methods suitable for deep water does not work. Hence, application of SRME or the inverse-scattering based methods becomes ineffective for free-surface multiples elimination. Under these circumstances, successful application of these free-surface multiple removal methods requires an adequate extrapolation of the missing near-offset traces. Patent Application US 2011/0044127 teaches a method of removing free-surface effects without the need of near-offset extrapolation, but requires more than one receiver cable and a seismic source at least 100 m in the front end of the spread. These constraints impose additional acquisition effort not required in a standard marine survey. Patent Application US 2011/00002539 teaches a method of zero offset seismic trace construction, but requires the deployment of additional receivers to record of the near-field acoustic source and does not specifically address the issue of free-surface multiples removal. What is needed therefore is a method that uses data from a standard marine survey and does not require extra acquisition effort (deployment of multiple cables or near-field receivers).